Effects of a Trapping Field on Microbubble Flow Dynamics

Fig. 3.6 shows representative images acquired for, from top to bottom, water only,

free-flowing microbubbles, microbubbles with the trapping field and microbubbles in combination with the control ARF beam. Schematic diagrams of PNP profiles across

the vessel axis are added to Fig.3.6(c) and (d).

In the presence of microbubbles, colour coded vector maps were superimposed onto their corresponding grey scale images reconstructed from single plane-wave pulses.

These grey scale images are shown with a dynamic range of 40 dB in Fig. 3.6. The

orientation of each arrow indicates the averaged interframe microbubble trace within that kernel, whilst the arrow length correlates the speed. In velocity estimations, the interrogation window occupied a depth span of 0.621 mm and a lateral width of 1.800

mm (see Table 3.4). The axial kernel overlapping of 50% was used for still vector flow

frames in Fig. 3.6. Two adjacent plane-wave RF frames were needed to resolve a single

vector flow frame, and no multi-frame averaging was applied to smooth the velocity profile.

Fig. 3.6(a) is a reference frame without microbubbles. The ROI within the flow

channel showing microbubble trajectories was defined with dotted lines and utilised with all the data. The flow condition in this study was estimated to be steady (see

PNP profile along the vessel axis

Figure 3.6: Examples of captured frames for (a) water, (b) freely flowing microbubbles, (c) microbubbles with the acoustic trap, and (d) microbubbles with the control ARF beam. In the presence of microbubbles, composite images are shown with the vector flow overlay. Flow vectors with a velocity slower than 5 mm/s are highlighted with green dots.

Table 3.3) and the resulting laminar flow would follow a parabolic pattern, with zero

speed at the wall. With identical parameter sets used for Fig. 3.6(b)−(d), the noise

floor of vector flow mapping was determined by processing one reference dataset with

purified water pumped through the channel at a rate of 56 mL/min (see Section3.4.3).

Consequently, 1100 plane-wave RF frames (or 1099 vector flow maps) were used and the noise floor was found to be 1.2 ± 0.6 mm/s (mean value ± 3 standard deviations). To improve clarity, a threshold of 5 mm/s which is above the noise floor was used for labelling flow vector estimations as green dots, indicative of the occurrence of trapped microbubbles. Other values above the noise floor for velocity estimations could be used and the threshold of 5 mm/s was heuristically adopted for reporting. No flow direction information was available at these locations. The ROI was chosen to exclude flow vectors on the wall.

Supplementary Video S2 shows one example of the temporal evolution of microbub-

ble flow patterns with acoustic trapping (https://ieeexplore.ieee.org/document/

8361061). To reject noise mainly residing in the deep location, the SVD filter (De- men´e et al.,2015) was introduced when producing the video. Interleaving the acoustic trapping beam with plane wave imaging pulses resulted in non-uniform microbubble

flow speeds in the inlet, trap, and outlet regions (Fig.3.6). When the eigen-based SVD

filter was first applied to the global plane-wave data, the complex spatially-varying microbubble speed affected the consequential microbubble speckle pattern and compli-

cated the velocity estimation. The block-wise SVD filtering has been suggested (Song

et al., 2017) to tackle spatially-varying characteristics but with heavy computational burdens. To simplify the processing in this study, the beamformed plane-wave RF frames were divided into the contrast region and the tissue background, and only the tissue background was spatio-temporally processed to remove noise. Noise is supposed

to be described by high-order singular vectors which have smaller singular values (De-

men´e et al., 2015). The SVD filter order was chosen to be 10 from which the sin-

gular value curve starts to flatten (Song et al., 2017) as shown in Fig. 3.7. Flow

dynamics were tracked with the method detailed above. For Supplementary Video S2 (https://ieeexplore.ieee.org/document/8361061), the axial kernel overlapping of 50% was employed in velocity estimations and the video was played back at 25 fps.

To show the effect of the acoustic trap and control ARF beam on the flow pro- file, first a control experiment without any ARF beams was performed to calculate

Singular Vector Order

100 200 300 400 500 600 700 800 900 1000 1100

Normalized Sigular Value (dB)

-55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Singular Vector Order

10 20 30 40 50

Normalized Sigular Value (dB)

-40 -30 -20 -10 0

Figure 3.7: The singular value distribution for the data used in Supplementary Video S2. Inset: expanded view of the singular value distribution with a separation line showing the cutoff order of 10.

the baseline (Fig. 3.6b). Before the activation of ARF beams at t = 202 ms, there

are no visible green dots representing trapped microbubbles. Fig. 3.6(c) shows a

single snapshot of microbubble flow dynamics when the acoustic trap is active. Al-

though the microbubble flow changes with time (see Supplementary Video S2,https:

//ieeexplore.ieee.org/document/8361061), the speed of microbubbles reduces sig- nificantly within the trapping region, with green dots showing trapped microbubbles.

When compared with results by using the control ARF beam in Fig.3.6(d), the acous-

tic trap in Fig.3.6(c) enables more microbubble accumulation also in the lumen. Once

acoustic trapping beams ceased at t = 1801 ms, the microbubble trajectories follow

a laminar flow pattern similar to Fig. 3.6(b), as shown in Supplementary Video S2

(https://ieeexplore.ieee.org/document/8361061).

The two axial overlapping sizes in Table 3.4 were used to manipulate the density

of flow vectors within the unaltered ROI. In each trial, the number of green labels was counted with the vector flow frame 101 to 900, considering the period (from 202 to 1801 ms) with the application of ARF beams. The normalized values are portrayed

spreading the lateral axis as shown in Fig. 3.8. With the identical setup in velocity

mapping, in comparison to experiments with the control ARF beam, where the drag force overcomes the counterflow radiation force, the acoustic trap shows the enhanced

Figure 3.8: Normalized distributions of trapped microbubbles along the lateral axis are shown by summing green dots from vector flow maps. The mean value and standard deviation are given based on three repeated trials.

capability of microbubble accumulation (p < 0.05) for both conditions in Fig. 3.8.

3.5.2 Effects of a Trapping Field on Microbubble Signal Amplitude